Reactor on-off antineutrino measurement with KamLAND

The recent long-term shutdown of Japanese nuclear reactors has resulted in a significantly reduced reactor ${\overline{\nu }}_e$ flux at KamLAND. This running condition provides a unique opportunity to confirm and constrain backgrounds for the reactor ${\overline{\nu }}_e$ oscillation analysis. The data set also has improved sensitivity for other ${\overline{\nu }}_e$ signals, in particular ${\overline{\nu }}_e$’s produced in $\beta$-decays from ${}^{238}\mathrm{U}$ and ${}^{232}\mathrm{Th}$ within the Earth’s interior, whose energy spectrum overlaps with that of reactor ${\overline{\nu }}_e$’s. Including constraints on ${\theta }_{13}$ from accelerator and short-baseline reactor neutrino experiments, a combined three-flavor analysis of solar and KamLAND data gives fit values for the oscillation parameters of ${tan}^2{\theta }_{12}={0.436}_{-0.025}^{+0.029}$, $\Delta m_{21}^2={7.53}_{-0.18}^{+0.18}\times {10}^{-5}{\mathrm{eV}}^2$, and ${sin}^2{\theta }_{13}={0.023}_{-0.002}^{+0.002}$. Assuming a chondritic Th/U mass ratio, we obtain ${116}_{-27}^{+28}$ ${\overline{\nu }}_e$ events from ${}^{238}\mathrm{U}$ and ${}^{232}\mathrm{Th}$, corresponding to a geo ${\overline{\nu }}_e$ flux of ${3.4}_{-0.8}^{+0.8}\times {10}^6{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$ at the KamLAND location. We evaluate various bulk silicate Earth composition models using the observed geo ${\overline{\nu }}_e$ rate.

Figure 1

Schematic diagram of the KamLAND detector. The shaded region in the liquid scintillator indicates the volume for the ${\overline{\nu }}_e$ analysis after the inner balloon was installed.

Figure 2

Time evolution of expected and observed rates at KamLAND for ${\overline{\nu }}_e$’s with energies between (a) 0.9 and 2.6 MeV and (b) 2.6 and 8.5 MeV. The points indicate the measured rates in a coarse time binning, while the curves show the expected rate variation for reactor ${\overline{\nu }}_e$’s (black line), reactor ${\overline{\nu }}_e$’s $+\mathrm{\text{backgrounds}}$ (colored line), and reactor ${\overline{\nu }}_e$’s $+\mathrm{\text{backgrounds}}+\mathrm{\text{geo}}$ ${\overline{\nu }}_e$’s (gray line). The geo ${\overline{\nu }}_e$ rates are calculated from the reference model [18]. The vertical bands correspond to data periods not used in the analysis. In the right panel of (a), the data are grouped according to periods of similar expected reactor ${\overline{\nu }}_e+\mathrm{\text{background}}$ rates, as denoted by the colored bands. The observed event rate for each group is plotted at the exposure-weighted expected event rate within the group. The efficiency-corrected best-fit value of the geo ${\overline{\nu }}_e$ rate from the full spectral analysis (dashed line), its $1\sigma$ error (shaded region), and the model expectation (gray line) are drawn for comparison. The contribution of geo ${\overline{\nu }}_e$’s in (b) is negligible. The oscillation parameters used to calculate the expected reactor ${\overline{\nu }}_e$ rate are the best-fit values from the global oscillation analysis: ${tan}^2{\theta }_{12}={0.436}_{-0.025}^{+0.029}$, $\Delta m_{21}^2={7.53}_{-0.18}^{+0.18}\times {10}^{-5}{\mathrm{eV}}^2$, and ${sin}^2{\theta }_{13}={0.023}_{-0.002}^{+0.002}$.

Figure 3

Prompt energy spectrum of ${\overline{\nu }}_e$ candidate events above the 0.9 MeV energy threshold (vertical dashed line) for each data-taking period. The background, reactor and geo ${\overline{\nu }}_e$ contributions are the best-fit values from a KamLAND-only analysis. The prompt energy spectra of ${\overline{\nu }}_e$ candidate events in the low-energy region are also shown in the inset panels with a finer binning. The top panel shows the energy-dependent selection-efficiency curves for each period.

Figure 4

Allowed regions projected in the $({tan}^2{\theta }_{12},\Delta m_{21}^2)$ plane, for solar and KamLAND data from the three-flavor oscillation analysis for (a) ${\theta }_{13}$ free and (b) ${\theta }_{13}$ constrained by accelerator and short-baseline reactor neutrino experiments. The shaded regions are from the combined analysis of the solar and KamLAND data. The side panels show the $\Delta {\chi }^2$ profiles projected onto the ${tan}^2{\theta }_{12}$ and $\Delta m_{21}^2$ axes.

Figure 5

Ratio of the observed ${\overline{\nu }}_e$ spectrum to the expectation for no-oscillation versus $L_0/E$ for the KamLAND data. $L_0=180\mathrm{km}$ is the flux-weighted average reactor baseline. The 3-$\nu$ histogram is the best-fit survival probability curve from the three-flavor unbinned maximum-likelihood analysis using only the KamLAND data.

Figure 6

Prompt energy spectrum of the ${\overline{\nu }}_e$ events in the low-energy region for all data-taking periods. Bottom panel: Data together with the best-fit background and geo ${\overline{\nu }}_e$ contributions. The fit incorporates all available constraints on the oscillation parameters. The shaded background and geo ${\overline{\nu }}_e$ histograms are cumulative. Middle panel: Observed geo ${\overline{\nu }}_e$ spectrum after subtraction of reactor ${\overline{\nu }}_e$’s and other background sources. The dashed and dotted lines show the best-fit U and Th spectral contributions, respectively. The blue shaded curve shows the expectation from the geological reference model of Ref. [18]. Top panel: The energy-dependent selection efficiency.

Figure 7

(a) C.L. contours for the observed number of geo ${\overline{\nu }}_e$ events. The small shaded region represents the prediction of the reference model of Ref. [18]. The vertical dashed line represents the value of $(N_{\mathrm{U}}-N_{\mathrm{Th}})/(N_{\mathrm{U}}+N_{\mathrm{Th}})$ expected for a Th/U mass ratio of 3.9 derived from chondritic meteorites. (b) $\Delta {\chi }^2$ profile from the fit to the total number of geo ${\overline{\nu }}_e$ events, fixing the Th/U mass ratio at 3.9. The grey band represents the geochemical model prediction, assuming a 20% uncertainty in the abundance estimates.

Figure 8

Geo ${\overline{\nu }}_e$ flux versus radiogenic heat from the decay chains of ${}^{238}\mathrm{U}$ and ${}^{232}\mathrm{Th}$. The measured geo ${\overline{\nu }}_e$ flux (gray band) is compared with the expectations for the different mantle models from cosmochemical [37], geochemical [11], and geodynamical [38] estimates (color bands). The sloped band starting at 7 TW indicates the response to the mantle ${\overline{\nu }}_e$ flux, which varies between the homogeneous and sunken-layer hypotheses (solid lines), discussed in the text. The upper and lower dashed lines incorporate the uncertainty in the crustal contribution.